Constant Curvature Algebras and Higher Spin Action Generating Functions

TL;DR

This paper introduces a new algebraic framework for higher spin theories on constant curvature manifolds, providing simplified generating functions for actions and gauge invariances, and revealing deep connections with algebraic structures and dimensional reduction.

Contribution

It develops a novel algebraic calculus for higher spin actions, gauge invariances, and their relation to algebraic deformations and dimensional reduction techniques.

Findings

Derived generating functions for higher spin actions and gauge invariances.

Reformulated higher spin theories in terms of a single scalar field in doubled dimensions.

Established a superalgebra framework for spinor-tensor fields.

Abstract

The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for the actions and gauge invariances of massive, partially massless and massless (for both bose and fermi statistics) higher spins on constant curvature backgrounds. These are formulated in terms of a minimal set of covariant, unconstrained, fields rather than towers of auxiliary fields. Partially massless gauge transformations are shown to arise as degeneracies of the flat, massless gauge transformation in one dimension higher. Moreover, our results and calculus offer a considerable simplification over existing techniques for handling higher spins. In particular, we show how theories of arbitrary spin in dimension d can be rewritten in terms of a single scalar field in dimension 2d where the d additional dimensions correspond to coordinate differentials. We also develop an analogous framework for spinor-tensor fields in terms of the corresponding superalgebra.